10: Principal Coordinates Analysis (PCoA)

Practice Task

Practice Task

Work through these questions after reading the Principal Coordinates Analysis chapter. The point of PCoA is that you choose the dissimilarity, so this task asks you to see how much that choice matters.

1. Compute a Bray-Curtis dissimilarity on the Doubs fish data and run a PCoA with capscale(spe ~ 1, distance = "bray"). Report the proportion of variation captured by the first two axes, and check the eigenvalues for negative (“imaginary”) values. If there are negative eigenvalues, explain why they arise and how they affect the proportions you reported.

2. Repeat the PCoA with a presence-absence dissimilarity (Jaccard or Sørensen) on the same data. Compare the two ordinations. How sensitive is the site configuration to the choice between an abundance-based and a presence-absence dissimilarity?

3. Use a Gower dissimilarity (cluster::daisy(..., metric = "gower")) on a table that mixes variable types, for example the Doubs environmental data treated together with one or more categorical variables of your own making. Run a PCoA on the result and explain why PCA and CA could not have analysed this table directly.

4. Run an nMDS on the same Bray-Curtis matrix from Question 1. Compare the PCoA and nMDS configurations, and state which method preserved the dissimilarities better, citing the appropriate goodness measure for each (proportion of variation / eigenvalue-based fit for PCoA, stress for nMDS).

5. On the basis of the above, write a short paragraph on when you would choose PCoA over PCA, CA, or nMDS.

Assessment Criteria

This Task is not formally assessed.